Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

Details Generalized Riemann minimal surfaces examples in three-dimensional manifolds products Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

2005-07-08

arxiv.org/abs/math/0507187v1

Mathematics

Differential Geometry

23 pages, 8 figures

Scientific paper

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in product manifolds $M \times \R$, where $M$ is the hyperbolic plane, the Euclidean plane or the two dimensional sphere. The main tool is the existence of a Jacobi field which characterize the property to be foliated in circles and geodesics in these product manifolds. It is related to harmonic maps.

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